Control method and apparatus for a UFC for minimizing input current distortions

ABSTRACT

In a pulse-width modulated unrestricted frequency changer (UFC) the harmonic contents of the input current are minimized by splitting the active time intervals within the fundamental time frame into at least two pulses which are located within such time frame and controlled in width as if individual PWM single-pulse UFC&#39;s were controlled having a phase shift between each other so as to eliminate or reduce undesired frequency components. Such elimination or minimization of selected frequency components is used to reduce the size of the lowpass filter at the input of the UFC, namely by allowing a higher cut-off resonance limit.

BACKGROUND OF THE INVENTION

The invention relates to static power frequency changers in general, andmore particularly to Unrestricted Frequency Changers (UFC) and theirapplications, for instance to adjustable speed AC motor drives.

The Unrestricted Frequency Changer (UFC) and its adjunct static switchcontrol for the generation of an AC wave of controlled voltage andfrequency have been described in U.S. Pat. Nos. 3,470,447 and 3,493,838of L. Gyugyi et al. These patents show how the switches in each of thestatic converters associated with an output phase of the load can beselectively and cyclically controlled for conduction during apredetermined time interval so as to derive and output power defined bya controlled increment of the input voltage, itself delineated betweentwo time intervals are used for shorting the output, which processresults in an AC output voltage having a frequency depending upon therepetition rate of the conduction time intervals and a magnitudemeasured by the time period of effective conduction of each staticswitch. Such an unrestricted frequency changer is advantageously appliedin variable speed AC drives as explained on pages 5-14, and 363-383 of"Static Power Frequency Changers" by L. Gyugyi and B. R. Pelly,published by John Wiley & Sons 1976. In this regard, for instance,Gyugyi and Pelly have observed that the UFC has an inherent bilateralcharacteristic between the powe source at its input and the power supplyat its output, which allows a four-quadrant operation of the motor drivewithout costly additional circuitry.

The unrestricted frequency changer technique has become particularlyattractive with the advent of modern bilateral switches, for instance,power transistors, and GTO devices.

When used for controlling the speed of an AC motor, the UnrestrictedFrequency Changer requires a voltage source type termination at theinput terminals. This is due to the fact that the AC motor represents aninductive load at the output. Since the UFC connects the multi-phaseinput source sequentially to such inductive load (thus, load current),the input source must provide low impedance path for the step-likecurrent wave drawn by the UFC. The voltage source type termination inpractice is normally provided by a low pass LC input filter in such away that the input terminals of the UFC are shunted by capacitors. Thistype of filter, viewed from the input terminals of the UFC, constitutesa parallel connected LC circuit, which provides a low impedance for thehigh frequency (harmonic) components present in the step-like UFC inputcurrent wave at frequencies higher than the resonant frequency of thecircuit. Thus, the basic criterion for the design of the filter is toensure that its resonant frequency (or "cut-off" frequency) is lowerthan the lowest input harmonic frequency (corresponding to the minimumoutput frequency) so as to avoid resonant amplification of the inputcurrent harmonics. This criterion often necessitates a relatively largeand expensive input filter.

The Unrestricted Frequency Changer (UFC) is an AC-to-AC converter. Inaddition to the fundamental current, extrabasal currents are generatedby the UFC flow through the input power line. Therefore, a properlydesigned input filter is essential to the pulse-width modulatedUFC-induction motor drive system. A method of filter design is known fora double pulse-width modulated 6-pulse UFC. The most difficult problemin the filter design, though, is that the low frequency extrabasalcomponents, where ω_(I) is the angular input frequency and ω_(O) is theangular output frequency, namely the (5ω_(I) +6ω_(O)) and (7ω_(I)+6ω_(O)) components, in the case of a 6-pulse UFC, are hard toeliminate. By increasing the modulation frequency, the magnitudes ofthese two low frequency components can be lowered to some extent.However, they still remain no matter how high the modulation frequencycan be increased. Another method of reducing the total rms extrabasalcurrent is to modulate each of the three UFC converters individually sothat between the output phases the control pulses are "interlaced", soas to minimize the overlap among neighboring pulses on the input side.This is the approach disclosed in concurrently filed copending patentapplication Ser. No. 06/596,329.

A preferable method would be to eliminate both the (5ω_(I) +6ω_(O)) andthe (7ω_(I) +6ω_(O)) components, in a 6-pulse UFC situation. Although aspecific example that it is possible does exist, it is not conceivable,at this time, that those two extrabasal components can be alwayseliminated for the whole range of the output voltage.

Assuming for the sake of discussion that elimination of only one of thetwo components, instead of two, in the UFC is possible, it will beeither the (5ω_(I) +6ω_(O)) component, or the (7ω_(I) +6ω_(O))component. Furthermore, if it is assumed that the relative amplitudes ofthose two components is being controlled, it becomes conceivable, then,to increase the cut-off frequency of the low-pass filter substantiallythereby to reduce the filter size and the VAR rating considerably. Inother words, it is possible to avoid, or at least mitigate, the effectof the filter resonance by controlling the extrabasal components whichare near to the cut-off frequency of the filter. Nevertheless, whenreducing one component, the amplitude of the other component isgenerally increased. In conclusion, this leaves still open therequirement of a total harmonic minimization method for a given filtercharacteristic.

SUMMARY OF THE INVENTION

It is the object of the present invention to provide an approach towardoptimization by which the input rms extrabasal current is minimized.Data are calculated, using a computer for several kinds of filterparameters and under particular UFC modulations.

Thus, the present invention pertains to a method and apparatus forcontrolling the output voltage of the UFC so as to ensure that the inputcurrent harmonics in a selected frequency range, in which the inputfilter exhibits a high impedance (resonance), remain minimal. Thisallows the resonant frequency of the input filter to be higher than thelowest input harmonic frequency. As a consequence, the size and cost ofthe input filter can be greatly reduced without significantly impairingthe distortion of the current drawn from the AC input source.

The present invention resides in controlling the bilateral switches ofan Unrestricted Frequency Changer (UFC), each switch upon its turn,within the switching cycle of the output phase so as to repeatedly andalternatively perform elementary conduction subintervals (t*) andsucceeding shorting sub-time intervals a predetermined n number of timeswith each switch and at distributed instants which in contrast to U.S.Pat. No. 4,488,216, are "unequally" spaced within the time period T ofoperation of the particular bilateral switch, the shorting timeintervals being varied in relation to the output frequency in such a waythat the amplitudes of the harmonic components, present in the outputvoltage and input current waveforms of a frequency that would be at, orclose to, the resonant frequency of the input filter, will be minimized.

Such control of the bilateral switches is accomplished digitally. Theallocation of elementary conduction time intervals to each bilateralswitch and their distribution throughout the time period thereof areperformed in accordance with a model which is taking into account theintended frequency and voltage at the output.

Digital techniques are used in order:

(1) to maintain a constant ratio between output voltage and frequencyfor constant airgap flux when applied to an induction motor;

(2) to provide substantially the same voltage increment as in a UFC ofthe prior art while selecting and allocating with unequal distributionwithin the time period T a number of elementary time intervals ofconduction per bilateral switch which equates with (t*) one timeinterval of conduction in the prior art, within the switching cycle perphase of the AC output wave.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an UFC motor drive system according toaforementioned U.S. Pat. Nos. 3,470,447, and 3,493,838;

FIG. 2 is a chart illustrating with curves the effect of three differentrepetition rates and spacings of the control pulse trains P1, P2 of thesystem of FIG. 1 upon the output frequency and voltage and upon theoutput current;

FIG. 3A shows the three phases of FIG. 1 associated with the load;

FIG. 3 shows with curves the operation of the system of FIG. 1 and FIG.3A without exercising any control of the commutated switches of theconverters for the purpose of adjusting the magnitude of the outputvoltage whereas, for comparison purpose;

FIG. 4 shows with curves how the control pulse trains P1 and P2 of thesystem of FIG. 1 establish controlled periods of conduction delineatedbetween controlled shorting periods to adjust the magnitude of theoutput voltage;

FIGS. 5A-5C are charts with curves comparing the three phases of the UFCsystem of FIG. 1;

FIGS. 6A-6C give a set of curves illustrating the effect at a reducedoutput voltage level upon one of the input supply lines with the priorart mode of control;

In FIG. 7 are juxtaposed voltage and current curves illustratingconduction periods of increased duration and their effect on theharmonics of the input currents drawn from the AC power source;

FIGS. 8A-8C illustrate with curves the output voltage control methodaccording to U.S. Pat. No. 4,488,216;

FIG. 9 shows with curves for an increasing number of conductionsubintervals how the motor current "ripple" decreases;

FIG. 10 parallels FIG. 9 by showing the corresponding change in theinput current waveform;

FIG. 11 shows the UFC output voltage waveform for two conductionsubintervals;

FIGS. 12A and 12B illustrate with curves single pulse-width modulationof a 6-pulse UFC system in cases #1 and #2, respectively;

FIG. 13 is the case #1 single pulse-width modulation of FIG. 12Aillustrated with edge definition by angles α₁, α₂ ;

FIG. 14 is the case #2 single pulse-width modulation of FIG. 12Billustrated with edge definition by angles α₃, α₄ ;

FIG. 15A is the double-pulse modulation situation when M=2 (two-pulse)in type A;

FIG. 15B is like FIG. 15A but in type B;

FIGS. 15C and 15D are like FIGS. 15A and 15B but for M=3 (three-pulse)in types A and B, respectively.

FIG. 16 shows a parallel-R-type second-order lowpass filter as can beassociated with the UFC system when practicing the invention;

FIG. 16A is the resonance characteristic of the filter of FIG. 16 whenω_(r) =6ω_(I) and Q=2;

FIG. 17 illustrates the two pulses of a double-pulse PWM UFC system withtwo independent variables β and δ;

FIG. 18 illustrates the three-pulses of a three-pulse PWM UFC systemwith two independent variables β and δ;

FIG. 19 illustrates the four pulses of a quadruple UFC system with threeindependent variables β, δ₁, δ₂ ;

FIG. 20 shows the basic time frame and the conduction and shortingintervals in a "double-pulse" situation;

FIG. 21 shows the basic UFC converter with an input filter coupledthereto;

FIG. 22 illustrates the frequency variation of the two most significantinput current harmonics against the normalized output frequency f_(O)/f_(I) ;

FIG. 23 shows the variations of the angles δ and β against thenormalized output frequency;

FIG. 24 is a chart of curves showing the variation of the two mostsignificant amplitudes of the UFC input current components, and ther.m.s. sum of these components drawn from the AC supply via the inputfilter, against the normalized output frequency in percent;

FIG. 25 shows the same input current components for the case whereδ=30°, e.g., for equal shorting intervals;

FIG. 26 shows the basic time frame and the conduction and shortingintervals in a "triple-pulse" situation;

FIG. 27 is analogous to FIG. 26, in the "quadruple-pulse" situation;

FIG. 28 illustrates the variation of δ, and β, and FIG. 29 the inputcurrent components for the "triple-pulse" mode of FIG. 26;

FIGS. 30 and 31 correspond to FIGS. 28 and 29 in the "quadruple-pulse"mode of FIG. 27, respectively;

FIG. 32 shows in block diagram one mode of implementation of controlapparatus according to the invention for a UFC with minimum input linecurrent distortion;

FIG. 33 illustrates with curves the operation of the circuit of FIG. 32while providing illustration of quadruple, triple and double pulseimplementation; and

FIG. 34 is a more detailed block diagram for the implementation ofcontrol apparatus according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

For the purpose of illustration the invention will be described as partof an AC drive system. It is understood, however, that the UnrestrictedFrequency Changer (UFC) according to the invention can be used in avariety of industrial and other applications.

In the AC drive system of the preferred embodiment of the invention anUnrestricted Frequency Changer (UFC) is used to provide variablefrequency-variable voltage output power to control the speed of an ACinduction motor. In keeping with the volt-per-hertz characteristic ofthe induction motor, the fundamental output voltage is variedessentially in proportion with the output frequency. Such variation ofthe output voltage had been achieved up to now by simple pulse-widthvariation technique. This prior art approach resulted in increased motorcurrent harmonics and the occurrence of increased ripple in the inputsupply current at relatively low motor speeds. A new voltage controlmethod is now proposed which minimizes the input supply and motorcurrent ripples over the total speed (output frequency) range. Thisresults in significant improvement in motor performance at low speedsand economic benefits by reducing the input filtering requirements andmotor losses.

The Unrestricted Frequency Changer (UFC) described in U.S. Pat. Nos.3,470,447 and 3,493,836 as static "artificially" commutated frequencyconverters with variable output voltage is well known in the literature,and this prior art type of converter will be hereinafter designated asthe UFC.

When compared to other static power converters, the UFC has significantadvantages that make it particularly suitable for providing variablefrequency electric power to control the speed of AC motors. Theseadvantages can be listed as follows:

1. Single stage power conversion with bidirectional power flow (i.e.,power can flow either to or from the load). This permits regenerativebraking of the motor.

2. A wide output frequency range, which is not limited by the input(supply) frequency. That is, the generated output frequency can belower, higher, and equal to the input frequency.

3. The frequency spectrum of the output waveform is independent of theamplitude of the wanted fundamental component. Furthermore, thefrequencies of the "unwanted" (harmonic) components in the outputwaveform are widely separated from the fundamental frequency over thetotal output frequency range. This separation of the harmonicfrequencies from the fundamental increases "naturally" (i.e., withoutchanging the method of output voltage waveform construction) as thefundamental output frequency decreases. Thus the frequencies of theharmonic currents in the motor remain high relative to the fundamental,even at low speeds. Therefore the motor runs without cogging.

4. The output voltages of a three-phase converter are inherently inbalance. Nevertheless, individual control of the three output voltagesis possible.

5. The lagging (inductive) motor displacement power factor results inleading (capacitive) displacement power factor (with equal phase angle)at the AC supply. Therefore, unity output (load) displacement powerfactor is reflected back to the AC supply without change.

6. Control is simple, that is, the output frequency and voltage can becontrolled as shown in the Gyugyi et al patents by two appropriatelydisplaced pulse trains, both having the same even rate.

However, the Unrestricted Frequency Changer has the disadvantage thatwith the prior art method of voltage control described in theabove-mentioned U.S. Patents, the amplitudes of the harmonic componentsin the output voltage, and those in the input current drawn from the ACpower supply, increase appreciably as the fundamental output voltage isdecreased. This results in increased losses in the machine at lowspeeds, and it may necessitate considerable filtering in the inputsupply lines. A method is now proposed, according to the presentinvention, by which the amplitude of the fundamental output voltage iscontrolled while maintaining an essentially constant amplitude ratiobetween the dominant harmonics and the fundamental voltage and currentat the output and input terminals of the UFC as the output voltage isvaried from maximum to zero.

The Unrestricted Frequency Changer (UFC) motor drive system described inthe aforementioned U.S. Patents, is illustrated schematically in FIG. 1.It consists of three identical bidirectional converter power circuits,CV₁, CV₂, CV₃, supplying the three stator windings W₁, W₂, W₃, of aninduction motor M, a gating logic GL generating the electrical signalsnecessary to turn ON and OFF the bilateral switching units (A₁, A₂, B₁,B₂, C₁, C₂) in each of the converters CV₁, CV₂, CV₃. A timing wavegenerator TWG is provided outputting two pulse trains P₁, P₂ in responseto external analog signals which determine through a setpoint SP theoutput frequency f_(O) and voltage V_(O) applied to the motor. Therelationship between the two control pulse trains P₁, P₂ and the outputvoltage V_(O) of the UFC is illustrated by the waveforms (a), (b), (c)shown in FIG. 2. As seen by (a), pulse train P₁ determines the outputfrequency and in accordance with (b) pulse train P₂ determines theamplitude V_(O) of the fundamental output voltge. The two pulse trainsare so coordinated that the output voltage V_(O) increases withincreasing output frequency f_(O) so as to maintain an essentiallyconstant air-gap flux in the motor. FIG. 1 illustrates gating by thegating logic circuit GL of the gate drive circuit of switching unit A₁within converter CV₁, switching unit A₁ having a GTO device mounted forbilateral operation. Switching unit A₁ is illustrative of the otherswitching units A₂, B₁, B₂, C₁ and C₂.

It appears from curve (c) of FIG. 2, that between two consecutive pulsesP₁, P₂ a segment of one of the input voltage waves provided by the inputAC power source is connected to the output of the converter by the gatedbilateral switches (A₁, A₂, B₁, B₂, . . . or C₂). Between twoconsecutive pulses P₂ and P₁, the output of the converter is shorted bythe bilateral switches. Such successive "segments of voltage" arederived from the input and applied to the output according to a definiteconduction pattern which involves six consecutive different bilateralswitches such as A₁ shown in the example of FIG. 1. Such successive"segments of voltage" are building up an alternating output voltageV_(O) with an essentially sinusoidal envelope, as shown, for differentoutput frequencies f_(O) =1/3f_(I), f_(O) =f_(I) and f_(O) =5/3f_(I), bycurve (c) of FIG. 2. The average of the "voltage segments" caused byconduction of a bilateral switch (A₁, A₂, B₁ . . . C₂) between twosuccessive pulses P₁, P₂ (shown on FIG. 2 under (a) and (b),respectively) varies essentially sinusoidally over the output cycle asillustrated by the dotted line under (c) in FIG. 2. The motor currenti_(O) due to the converter output voltage V_(Of) as shown in FIG. 2under (c) is illustrated in FIG. 2 by curve (d). The dotted line thereshows the fundamental component i_(Of) of the motor current i_(O).

The switching pattern depends upon the time interval between twoconsecutive pulses P₁, P₂ as well as upon the repetition rate of the twotrains of pulses. In order to maintain a constant air-gap flux in themotor, when the frequency f_(O) increases (increased repetition rate ofP₁, P₂) the voltage V_(O) is automatically increased by spacing more P₁and P₂ from one another, thereby increasing the width of each "voltagesegment". This is shown in FIG. 2 under (a), (b) and (c) for threeinstances of output frequency: f_(O) =1/3f_(I) ; f_(O) =f_(I) and f_(O)=5/3f_(I), where f_(I) is the frequency of the input AC power sourcesupplying the three converters CV₁, CV₂, CV₃.

FIG. 3A shows the UFC conncected with the three phases of the load.

The basic operating principles of the UFC will be better understood byreferring to the waveforms shown in FIGS. 3 and 4 for one of the threeoutputs of the UFC. The basic output voltage waveform V_(O) of the UFC,ignoring for the moment the control of the magnitude of the fundamentalcomponent, can be generated by allowing the pairs of switching units A₁B₂, A₁ C₂, B₁ C₂, B₁ A₂, C₁ A₂, C₁ B₂ to conduct, in that sequence, fora fixed period of time T, so that each of the input line voltages beconnected in turn across the load during that pause period of time. Thesequence is repeated at a predetermined repetition rate. As illustratedin FIG. 3, such repetitive switching pattern extends over a time periodTP defined by the consecutive uniform time frames T, individuallyindicated at T₁, T₂, T₃, T₄, T₅, and T₆. This switching pattern providesan output voltage wave V_(O) having a "wanted" fundamental componentV_(F) with a frequency f_(O) equal to the difference between the ACsupply frequency f_(IN) and the repetition frequency f_(SW) of theswitching pattern, as explained in the above-mentioned patents.

While FIG. 3 illustrates the operation of a system in which for eachbilateral switching unit the conduction interval (T) extends fullybetween two consecutive switching points NC, e.g. between two ON-comingstatic switches in the succession (A₁ B₂, A₁ C₂, B₁ C₂, . . . C₁ B₂),FIG. 4 illustrates a system in which the duration of conduction (T) iscontrolled, e.g. reduced from such maximum duration T to t₁. As shown inFIG. 4 this is achieved by shorting the output terminals, that is, theload, during a complementary time interval t₂ =(T-t₁). This is achievedby the pair of switches connected to the same input line (A₁ A₂, C₁ C₂,. . . B₁ B₂). Such width-control of t₁ within T allows the control ofthe fundamental output voltage, as explained in either of the twoaforementioned patents. This mode of control is characterized by arepetitive switching pattern extending over the time period TP that isdefined by six uniformly spaced time frames T labeled T₁ through T₆. Intime frame T₁, power switches A₁ and B₂ are turned on for the timeinterval t₁. At the end of the interval t₁, switches A₁ and A₂ areturned on for the duration of interval t₂ to short the load and therebyprovide a path for the load current. In the next time frame T₂, switchesA₁ and C₂ are turned on for the duraction of interval t₁ to apply inincrement of input voltage V_(AC) to the load. At the end of interval t₁of time frame T₂, switches A₁ and C₂ are turned off and switches C₁ andC₂ are turned on for the duration of interval t₂ of the same time frameto short the load. The rest of the sequence in the switching patternshould be apparent from examination of FIG. 4. It is also obvious fromthe figure that pulse train P₁ defines the time frame T, and thereby theoutput frequency of the fundamental or wanted output voltage V_(F) ofoutput voltage wave V_(O), whereas pulse train P₂ defines the relativelength of invervals t₁ and t₂, in the given time frame T, and thusdetermines the amplitude of the fundamental component V_(F).

The switching pattern for the three phases of a complete three-phase UFCis shown in FIG. 5 and in FIGS. 6A-6C. The current wave i_(A), soderived from one of the input lines (A) at a reduced output voltagelevel V_(A), is illustrated under (f) in FIG. 6C.

One disadvantage of the prior art UFC is that the amplitude of theharmonics in the so derived input current wave i_(A) (and thus for thetotal rms current distortion) increase as the fundamental components ofthe output voltage V_(A) is decreased by means of decreasing timeinterval t₁, as illustrated in FIG. 7. The reason for this is that atconstant rated output current (which corresponds to the rated torque ofthe motor at any speed), the peak instantaneous values of the inputcurrent remain essentially the same (these being determined by theamplitude of the constant output current) whereas the average (orfundamental) input current decreases as the output voltage is decreasedat reduced motor speeds. (The power requirements of the motor at a fixedoutput current and at a reduced fundamental output voltage is providedby the AC input supply at a fixed input voltage and at a reducedfundamental input current). In the prior art UFC, the average input linecurrent is reduced by decreasing the "active" time interval, t₁, duringwhich voltage is applied to the motor and current is drawn from the ACsupply. Since the average (or fundamental) output voltage approacheszero, the input current becomes composed of a number of narrow currentpulses, the width of which approach zero while the zero current (or"passive") interval t₂ deferred between those pulses approaches thelength of the basic time frame T as the "active" conductive timeinterval t₁ approaches zero.

The frequencies of the harmonic current components can be expressed interms of the input supply frequency, f_(I), and the generated outputfrequency, f_(O), as follows:

    f.sub.n =6mf.sub.O +(6m±1)f.sub.I, m=1,2,3, . . .       (1')

where f_(I) is the input supply frequency and f_(O) is the generatedoutput frequency applied to the motor. At a fixed input frequency, theharmonic frequencies increase with the output frequency from theirminimum values of (6m±1)f_(I). These minimum values correspond to theodd harmonic frequencies: 5f_(I), 7f_(I), 11f_(I), 13f_(I), etc.

From the frequency spectrum (1') it follows that the input filter whichis required because a practical input supply would have a non-zero,usually inductive source impedance, would have to have a "cut off" (orresonant) frequency that is lower than 5f_(I) --typically it would be4f_(I) --if the speed of the motor and accordingly the output frequencyof the UFC, is to be varied from zero to some maximum value.

A control method is now proposed which, in addition to providing acontinuously variable output voltage, allows minimizing the amplitude ofselected current harmonics. The basic idea is to minimize the amplitudesof input current components of a frequency which would be at, or closeto, the resonant frequency of the LC input filter, thereby to preventharmonic amplification, as the output frequency of the UFC is variedover the specified range. The proposed control method also provides asignificant overall improvement in the quality (distortion) of both theoutput voltage and input current waveforms over that characterizing theaforementioned prior art UFC.

The gist of the output voltge control method according to the inventioncan best be understood first from a comparison of prior art curves (a)to (c) in FIG. 8.

Under (a), the voltage curves for V_(BC), V_(BA), V_(CA), V_(CB) are theenvelopes of the UFC output voltage V_(O), where the switches areconnected the AC input supply voltages in sequence for uniform timeduration T to the output (load) without the provision of means forcontrolling the amplitude of the fundamental component.

Under (b), with the voltage control effected according to one prior artmethod, as explained previously, the uniform time durations T aresubdivided into two intervals t₁ and t₂. During interval t₁, the inputsupply voltages are, as before, connected to the output by the switchesof the power converter. During time intervals t₂, the input supplyvoltages are disconnected and the load is shorted by the switches of thepower converter. The relative lengths of intervals t₁ and t₂ within thebasic time duration (or time frame) T determine the amplitude of thefundamental output voltage generated by the UFC.

Under (c), the prior art basic control technique used according toequally spaced subintervals (t*), is illustrated. The uniform timedurations T are subdivided into n (n equals four in FIG. 8) subintervalsof durations T₁ ^(*), T₂ ^(*), T₃ ^(*), . . . T_(n) ^(*) such that:##EQU1## Each subinterval T₁ *, T₂ *, T₃ * , . . . , T_(n) is in turnsubdivided into two intervals t₁₁ * and t₁₂ *, t₂₁ * and t₂₂ *, t₃₁ *and t₃₂ *, . . . , t_(n1) * and t_(n2) *, that is: ##EQU2##

During such time intervals t₁₁ *, t₂₁ *, t₃₁ *, . . . t_(n1) *, withineach time frame T, the same input supply voltage, which is occurringfrom the input side in the normal UFC sequence, is connected repeatedlyn times to the output, whereas during time intervals t₁₂ *, t₂₂ *, t₃₂*, . . . , t_(n2) *, the input supply voltage is disconnected from theoutput, the load being as before, shorted. Since t₁₁ *+t₁₂ *+t₁₃ *+ . .. +t_(1n) *=t₁ and t₂₁ *+t₂₂ *+t₃₂ *+ . . . t_(n2) *=t₂, it is evidentthat the fundamental component of the output voltage wave will be thesame as obtained under (a).

The simplest form of control is obtained when all of the subintervals ofthe same kind are made equal. This is the mode of control disclosed inU.S. Pat. No. 4,488,216.

In such case:

    T.sub.1 *=T.sub.2 *=T.sub.3 *= . . . =T.sub.n *=T*

    t.sub.11 *=t.sub.21 *=t.sub.31 *= . . . =t.sub.n1 *=t.sub.1 *

    t.sub.12 *=t.sub.22 *=t.sub.32 *= . . . =t.sub.n2 *=t.sub.2 *

and

    nt*=T

    nt.sub.1 *=t.sub.1

    nt.sub.2 *=t.sub.2

For identical subintervals, it can be shown that the amplitudes of themost significant harmonics (i.e., those whose frequencies are thelowest) present in the output voltage and in the input current wavesdecrease significantly (in contrast to control without subdividing theactive interval of conduction into subintervals where the amplitudes ofthe most significant harmonics increase), when the amplitude of thefundamental output voltage is decreased. In particular, if n=2, theamplitudes of the output voltage components with frequencies of (6f_(I)+5f_(O)) and (6f_(I) +7f_(O)), and those of the related input currentcomponents with (6f_(O) +5f_(I)) and (6f_(O) +7f_(I)), decreasemonotonously with decreasing output voltage. It is emphasized again thatthis is in contrast to the prior art where the amplitudes of suchharmonics generally increase with decreasing output voltage. It shouldbe mentioned here that the output voltage and input current harmonics ofthe UFC are closely related. That is, the frequencies of the harmoniccomponents present in output voltage and input current waveforms can bedescribed by a similar mathematical expression:

    f.sub.n output voltage =6mf.sub.I +(6m±1)f.sub.O        (2')

where (m=1,2,3 . . . ) and

    f.sub.n input current =6mf.sub.O +(6m±1)f.sub.I         (3')

where (m=1,2, . . . )

Furthermore, the amplitudes of the related output voltage and inputcurrent harmonics vary in a similar manner with the variation of thefundamental output voltage.

As n increases (n=2,3,4 . . . ), both in the output voltage and inputcurrent waves, the number of harmonics, the amplitude of which decreasesin proportion with the decreasing output voltage, increases. As shownfor n=2, there are two such components. For n=3, there are four, forn=4, there are six, both in the output voltage and input current waves.These components can be obtained from the expressions (1'), (2') (3') off_(n) voltage and f_(n) current by substituting m=n-1. As a result ofthe harmonic reduction, the motor current i_(Of) has a "ripple" i_(o) towhich decreases rapidly as the number n of the subdurations T* isincreased from one to two, three and four within a basic time frame T ata given output frequency f_(O), as illustrated in FIG. 9. The change inthe input current waveform i_(A) when increasing n from one to four isillustrated in FIG. 10. It can be observed that the "envelope" of theinput current wave at n=4 is similar to that obtained at full outputvoltage. Therefore, it is evident that the low order harmonics do notincrease, as they do without such n subintervals, when the outputvoltage is decreasing.

With the prior art control method in which all the conductionsubintervals t₁ * are kept identical and all shorting subintervals t₂ *are kept identical, the amplitudes of the lowest order input harmoniccurrents are reduced approximately in proportion to the reduction of thefundamental component. However, the amplitudes of these components stillwill remain greater than zero at any output frequency. Therefore,although the input filtering requirements are reduced, the cut off(resonant) frequency of the input filter still has to be kept below thefifth harmonic to avoid resonance.

Accordingly, an improved control method is now proposed by which theshorting intervals will no longer be kept identical but rather arevaried with the output frequency in such a way that the amplitudes ofthose components having a frequency which would be at, or close to, theresonant frequency of the input filter is minimized.

The concept on which rests the control method according to the inventioncan be explained with reference to FIG. 11, where a UFC output voltagewaveform with two conduction subintervals (t₁ *) ("double" pulse) withinthe basic time frame (T) is shown. If the output voltage waveformcorresponding to the first conduction interval (shown "unfilled") andthat corresponding to the second conduction interval (shown "filled")are considered separately, then essentially two output voltage waveformsof the prior art UFC are produced. These waveforms are phased shiftedwith respect to one another, so that all the shorting subintervals (t₂*) are equal. Each output voltage waveform contains the harmoniccomponents with the same frequencies 6f_(I) +5f_(O), 6f_(I) =7f_(O),12f_(I) +11f_(O), 12f_(I) +13f_(O), etc. However, these harmoniccomponents are in fact phase-shifted with respect to each other. As aresult they "weaken" each other. In other words, the vectorial sum oftwo harmonics having the same frequency results in an amplitude that islower than the algebraic sum of the amplitudes which would be obtainedif the output waveform had been constructed with single conductionintervals of double width as in the prior art UFC. It is easy tovisualize, and it can be shown mathematically, that any particularharmonic component in the "double pulse" (two conduction subintervals inthe basic time frame) can be cancelled out by selecting such shortingsubintervals between subsequent active intervals in the time frame as toproduce a 180° relative phase shift for the selected harmonic in the"unfilled" and "filled" output waveforms.

More generally, it is observed that wherever multiple pulses are used tomodulate a UFC system, such multiple-pulse-width-modulated (PWM) UFCoperation can be represented as the sum of single-pulse-width-modulated(PWM) UFC systems. It is also observed that there are two kinds ofmodulation modes in a single-PWM UFC system.

These two modes will be referred to hereinafter as case #1 and case #2.These two situations are illustrated by FIG. 12A (case #1) and FIG. 12B(case #2). The illustration is made in the siaution of a y-pulse UFC.The existence functions in those two cases are defined as follows:

Case #1

The line-to-line existence function of g₁₁ is defined by angles (α₁, α₂)expressed in degrees with respect to the respective edges of the voltagemodulation slice, as shown in FIG. 14 and as follows: ##EQU3##Therefore, from relations (1), (2) and (3), it follows that: ##EQU4##Since ##EQU5## relation (4) leads to: ##EQU6##

Case #2

In the 6-pulse UFC, the modulation limits are (-π/6, π/6). If the pulsesare separated, as shown in FIG. 14, by these modulation limits, the casecan be considered as another kind of single pulse-width-modulated UFC.In this case, the line-to-line existence function can be represented as:##EQU7## Therefore, relations (6) and (7) lead to: ##EQU8##

The existence functions just defined can be used to obtain the 6-pulsevoltage v_(o). Thus, the existence functions for case #1 and case #2 aregiven by relations (5) and (8), respectively. The following is assumed:

    α.sub.2 -α.sub.1 =β.sub.1 (α.sub.2 +α.sub.1)/2=δ.sub.1

    α.sub.4 -α.sub.3 =β.sub.2 (α.sub.4 +α.sub.3)/2=δ.sub.2                           (9)

then relations (5) and (8) become:

(1) for case #1: ##EQU9##

(2) for case #2: ##EQU10## Then, the output voltage v_(o) is given by##EQU11## where v_(lp) represents the line-to-line voltage at the input,namely:

    v.sub.lp =V.sub.LL cos (ω.sub.I t-2pπ/3).

From relations (10) and (12), it follows that the output voltage forcase #1 is: ##EQU12## then relation (13) becomes ##EQU13## For a 6-pulseoutput, this reads: ##EQU14## Similarly, the output voltage for case #2is: ##EQU15## These two expressions of the 6-pulse voltage underrelations (15) and (16) belong to two different singlepulse-width-modulated 6-pulse UFC systems. The output voltageexpressions for the multiple PWM UFC cases can be generally obtained bythe sum of such single pulse-width-modulated expressions provided aproper phase shift is accounted for. As in the case of a singlepulse-width-modulated UFC, there are two kinds of multiple PWM UFC's. Ifone of the multi-pulses is separated by the modulation limits (±π/6),the expressions for the multiple PWM UFC's can be obtained by the sum ofcase #1+case #2 (referred to as Type B). Otherwise, they can beexpressed by the sum of case situations only (referred to as Type A).

Type A

For M blocks of pulses, the expressions for the type A becomes ##EQU16##

Type B

For the Type B, it becomes ##EQU17## The corresponding waveforms areillustrated in FIGS. 15A-15D. FIG. 15A shows Type A, with M=2. FIG. 15Bshows type B with M=3. Whereas FIG. 15C is Type A with M=3 and FIG. 15Dis Type B with M=3.

The above expressions (17) and (18) are more general than the precedingones.

The input current for a 6-pulse UFC system can be derived from theline-to-line existence functions given by relations (10), (11). In orderto get the line-to-neutral current in the input, the line-to-linecurrent i_(I)Δ is first being calculated as follows: ##EQU18## and whereI_(o) is the peak phase current of the load.

For the type 1 single pulse-width-modulated case, i_(I) can becalculated from relations (10), (19) as follows: ##EQU19## For a 6-pulseUFC system, the line-to-line input current becomes: ##EQU20## Fromrelation (21), the phase current i_(I1) is obtained as follows:##EQU21## Like in the case of the output voltage, the input phasecurrent for the type A multiple pulse-width-modulation (under M blocks)is given by the sum of the case #1 single pulse-width-modulated currentswhich are given by relation (22). Therefore: ##EQU22## Similarly, theinput phase current for type B multiple pulse-width-modulation is givenby ##EQU23##

A filter is required at the input of a UFC system. It is generally asecond order lowpass filter. FIG. 16 illustrates a parallel-R-typesecond-order lowpass filter, including an LR parallel network in thehorizontal branch and a capacitor C in the vertical branch, where thefiltered input current is i_(IF), with an input voltage v_(I) and offiltered voltage v_(IF) and output current i_(I).

The transfer function of such a filter is given by ##EQU24## Thesecond-order lowpass filter characteristic according to equation (25) isplotted in FIG. 16A, for ω_(r) =8ω_(I) and Q=2 for the purpose ofillustration.

Similar characteristics are readily ascertained by experience andcalculations for ω_(r) =8ω_(I) and for Q=10, for instance, for ω_(r)=6ω_(I) and Q=10 or ω_(r) =8ω_(I) and Q=2, as well.

From relations (23) to (25), the filtered input current i_(IF) isderived as follows: ##EQU25## The filtered total harmonic rms current inthe input, i_(HR), is given by: ##EQU26##

If the existence functions are centered on 0 degrees ([-π/6, 0], [0,π/6]) are symmetrical, then: ##EQU27##

The harmonic rms current in such symmetrical modulation situation can beobtained from relations (27) and (28) as follows: ##EQU28##

In order to reduce filter size, it is necessary to increase the resonantfrequency. At the same time, filter insertion loss and excessiveextrabasal currents due to the resonance should be minimized. It isalmost impossible to meet all such requirements with a conventionalsymmetrical fixed angle modulation of a UFC system. If the two lowestcomponents, (5ω_(i) +6ω_(o)) and (7ω_(I) +6ω_(o)), could both beeliminated by proper modulation, it would be possible. Unfortunately,such a favorable condition for all range of output voltages do notexist. As an alternative, one of the two components only can beeliminated for all range of output voltages if the proper modulationmethod is used. As a compromise, though, using this characteristic andcombining with a lowpass filter, will allow substantailly to reduceextrabasal current in the input side. An optimization modulation tominimize the filtered extrabasal current in the input is as follows:

Starting with nonlinear equations the zero solution can be sought byusing a linearization technique. A set of nonlinear equations is assumedto be:

    [f(X)]=0                                                   (30)

where:

    f=[f.sub.1, f.sub.2 . . . f].sup.T

    X=[X.sub.1, X.sub.2 . . . X.sub.N ].sup.T,

Then, equation (3) can be solved by iterative calculations with acomputer. The steps involved in computing a solution are as follows.

1. Guess a set of initial values for X, that is,

    X.sup.0 =[X.sub.1.sup.0, X.sub.2.sup.0, . . . X.sub.N.sup.0 ].sup.T.

(31)

2. Solve dX from the linearized equation: ##EQU29##

3. Repeat the above procedure using, as improved guesses,

    X.sup.1 =X.sup.0 +dX

until (3) is satisfied to the desired degree of accuracy. This processis a trial and error method. In case of divergence, or physicallymeaningless results, it is necessary to start with another initialguess. If the calculated stp size is too large, it is also necessary toreadjust the step size properly for better convergence.

If the set of nonlinear equations has zero solutions, the abovealgorithm is useful to solve it. However, in many cases there are nozero solutions. For an example, if the numbers of independent variablesare not equal to the numbers of nonlinar objective functions, the zerosolution cannot be found. In such case, sometimes it is useful to seekthe minimum point of the linear equations. By modifying theaforementioned algorithm for the zero solution, the minimum point can befound. If the initial guess is pretty far from the minimum point, thezero solution algorithm converges quickly. However, if it approaches tothe minimum point, it oscillates around that point, or sometimes itjumps far and goes to the other direction. In order to make it convergeto the minimum point, total error should be observed and the step shouldbe adjusted around that point. To do this, one more additional errorfunction is defined from relation (30) as follows:

    E=f.sub.1.sup.2 +f.sub.2.sup.2 + . . . +f.sub.N.sup.2.     (35)

The steps involved in such modified algorithm are as follows:

1. Guess a set of initial values given by (30).

2. Calculate error E₁ from (35) for X⁰.

3. Calculate an improved guess X¹ from the zero solution algorithmdescribed in previous section.

4. Calculate E₂ from (30) for X¹.

5. If E₂ ≦E₁, then repeat above procedure by replacing X⁰ to X¹.

6. If E₂ >E₁, then compare ε(=E₂ -E₁) with the predetermined desireddegree of accuracy. If it is satisfied, the minimum point is reached.

7. If ε is still large, reduce step size dX, calculate X¹ again from(34) and go to step 4.

In Appendix A, a subroutine program written in FORTRAN is provided underthe subroutine identification MINP.

In the case of an AC motor driven by the UFC, when minimizing the rmsharmonic current after filtering, constant flux operation of the motoris assumed, that is,

    V.sub.o /f.sub.o =constant.                                (36)

If we denote r as the normalized ratio of the output voltage, then rbecomes for the constant flux operation:

    r=V.sub.o /V.sub.b =f.sub.o /f.sub.b                       (37)

where V_(b) and f_(b) are the base voltage and the base frequency,respectively. For convenience, V_(b) =3/π V_(LL) and f_(b) =f_(I) inequations (17) and (18).

The optimization of the input extrabasal current including the inputfilter is performed for type A modulation of UFC. The input filter usedin this case is as shown in FIGS. 16 and 16A. The objective functionsfor the double, triple and quadruple modulations are given for thesymmetrical modulations and for the same widths of the pulses, are asfollows:

1. Double PWM UFC

From relations (17), (29), (36) and (37), it is seen that the twoobjective functions with two independent variables are defined for M=2as follows: ##EQU30## and δ=2δ₁. The existence function for this case isshown in FIG. 17.

Equation (38) defines control of the fundamental component from 0 tofull range by varying r, while equation (39) defines minimizing thesquare sum of the 5th and 7th components as r increases from 0.

2. Triple PWM UFC

In this case M=3 and the objective functions are defined as ##EQU31##Equation (41) defines control of the 5th, 7th, 11th and 13th componentsrelated to the filter characteristic. The existence function in thiscase is shown in FIG. 18.

3. Quadruple PWM UFC

In this case M=4 the objective functions have three independentvariables: ##EQU32## Equation (43) is the function for the 5th and the7th components, whereas equation (44) relates to the 11th and the 13thcomponents. The existence function in this case is shown in FIG. 19.

Reference is now made to FIG. 20 where the conduction intervals t₁ ^(*)(logic "high") and shorting intervals t₂ ^(*) (logic "low") are shownwithin a basic time frame T for a "double-pulse" (two conductionintervals) type of voltage control. The conduction intervals aresymmetrically spaced with respect to the center point of time frame T.For convenience, all intervals in FIG. 20 are shown in electricaldegrees, instead of actual times, in order to make the relationshipsindependent of the actual output and input frequencies. Thus, the timeframe T represents 60 electrical degrees at any output and inputfrequencies. As explained previously, the relationship between the giveninput frequency f_(I), the wanted output frequency f₀ and the requiredtime frame T can be expressed as follows: T=1/6 (f_(I) +f_(O)). Thus,the actual time corresponding to one electrical degree, at given f_(I)and f_(O), can be expressed mathematically as follows: 1°=T/60=1/360(f_(I) +f_(O)). In the double-pulse situation, βis the duration indegrees of each of the two active pulses, and δ is the separationbetween the axes of the two pulses.

If angle δ/2 is equal to 15°, then, all of the shorting intervals areequal to each other (a shorting interval is equal to δ-β, where βcorresponds to conduction time t₁ ^(*) and thus determines the amplitudeof the fundamental output voltage). In this case, as explained earlier,the dominant output voltage and input current harmonics havingfrequencies of (6f_(I) +5f_(O)), (6f_(I) +7f_(O)) and (6f_(O) +5f_(I)),(6f_(O) +7f_(I)), respectively, are reduced but not eliminated. However,if δ/2 is given the specific values of Table I herebelow, then, eitherof these two, or any other harmonic component can be eliminated totallyfrom the output voltage and input current waves:

                  TABLE I                                                         ______________________________________                                        Value of Angle δ/2                                                                       Component Eliminated                                         ______________________________________                                        18.00°     6f.sub.I + 5f.sub.O (output voltage)                                          5f.sub.I + 6f.sub.O (input current)                         12.86°     6f.sub.I + 7f.sub.O (output voltage)                                          7f.sub.I + 6f.sub.O (input current)                          8.18°    12f.sub.I + 11f.sub.O (output voltage)                                        11f.sub.I + 12f.sub.O (input current)                         6.92°    12f.sub.I + 13f.sub.O (output voltage)                                        13f.sub.I + 12f.sub.O (input current)                        ______________________________________                                    

The above relationships are used in the control strategy employed withthe method according to the invention, thereby to reduce significantlythe size of the input filter required for the UFC.

This control strategy for the UFC, as applied to a "double pulse" typeof control, can be explained by reference to FIG. 21, where the basicUFC power converter is shown, as generally known, to have associatedthereto an input filter consisting of a shunt capacitor C and a seriesinductor L in each phase. The inductor L can be the impedance of thesource itself.

As earlier stated, in practice a low pass input filter is needed tolimit the voltage transients at the input terminals, and across theconverter power switches, by providing a low impedance path for theinput current harmonics of the UFC. Such low pass LC input filterexhibits a resonance at the frequency determined by the value of L and Caccording to the expression f_(r) =1/(2π√LC). From a economicstandpoint, L and C should be as small as possible. The minimum value ofinductance L is usually given by the available AC power source. Thevalue and, thus, the size of C, are determined by design criteria, amongwhich the most important is the limit for the input current distortionallowed. The resonance of the LC input filter can very much increase theinput current distortion and, thereby affect the terminal voltage to thesame extent.

Referring to FIG. 22, the frequency variation for the two mostsignificant input current harmonics, mainly with frequencies of (5f_(I)+6f_(O)) and (7f_(I) +6f_(O)), is shown against the normalized outputfrequency f_(O) /f_(I). It can be seen that, as the output frequency isincreased from f_(O) =0 to f_(O) =f_(I), the frequencies of those twoharmonics increase from 5f_(I) to 11f_(I) and from 7f_(I) to 13f_(I),respectively. Therefore, in order to avoid resonant amplification ofboth of these harmonics, the cut-off (resonant) frequency of the LCinput filter in the prior art UFC must be lower than 5f_(I). Typically,it is chosen to be 4f_(I). With a given L (usually the supplyinductance), the minimum capacitor required can be determined with theselected cut-off frequency (f_(r) =4f_(I)) as follows: ##EQU33##

In order to use a smaller capacitor (which would mean higher filterresonant frequency) without any significant increase in the inputcurrent distortion, the amplitudes of the input current harmonics mustbe close to zero at frequencies for which harmonic amplification istaking place, due to the resonance of the input filter. Since in motordrive applications, which are a major field of application of the UFC,the output voltage is varied substantially in direct proportion to theoutput frequency (so as to keep the airgap flux in the motor constant),selected harmonic elimination in the input current is possible in thenormal course of output voltage control by appropriately establishinglocations within the basic time frame T for the conduction intervals inaccordance with a judicious selection of the control angle δ, asindicated earlier in Table I. Indeed, angle δ can be controlled so thatthe rms distortion of the current, drawn from the AC source by the UFCwith the input filter, remains minimum when the output frequency andvoltage are being varied.

The optimum values of angle δ, to obtain minimum input supply currentdistortions, have been calculated over the output frequency range ofzero to f_(I) (0≦f_(O) ≦f_(I)) for an input filter having a cut-off(resonant) frequency of f_(r) =6f_(I) and a quality factor of Q=10. Aneven multiple of the input supply frequency is chosen for the filtercut-off frequency, because even harmonics are normally absent in the ACsupply so that the input filter is not significantly burdened by the oddsupply harmonics. With a cut-off frequency of 6f_(I), and the same valueof L, the capacitance value and, thus, the size of the capacitor arereduced by a factor of 1-(4f_(I) /6f_(I))² =(1-4/9) or by 56%.

The results of the optimization process carried out to determine thevalues of angle δ require to keep the input current distortion of theUFC with the input filter at a minimum as the output frequency is variedfrom zero to f_(I). These results are shown in FIGS. 23 and 24. Asexplained earlier, the output voltage is assumed to vary in proportionwith the output frequency.

In FIG. 23, the variations of angles δ (DELTA) and β (BETA) are shownagainst the normalized output frequency f_(O) /f_(I). As can be seen,at, and in the vicinity of, f_(O) /f_(I) =0.166, that is, where f_(O)=0.166×f_(I), the angle δ becomes 36 degrees. At this value of δ (i.e.,δ/2=18°) the current harmonic with the frequency of 5f_(I) +6f_(O)becomes zero (refer to Table I). This is necessary to avoid resonantamplification since at f_(O) /f_(I) =0.166, the frequency of 5f_(I)+6f_(O) =5f_(I) +6×0.166f_(I) coincides with 6f_(I) the resonantfrequency of the input filter.

In FIG. 24, are shown the variations of the amplitude of the UFC inputcurrent components with frequencies of 5f_(I) +6f_(O) and 7f_(I)+6f_(O), together with the rms sum of these components drawn from the ACsupply via the input filter. In FIGS. 23 and 24: curve (1) representsthe filtered rims of the 5th and the 7th components; curve (2) is theunfiltered components of (5f_(I) +6f_(O)) while curve (3) is theunfiltered component of (7f_(I) +6f_(O)). It is observed that thecomponent 5f_(I) +6f_(o) does indeed become zero in the vicinity off_(O) /f_(I) =0.17 and thus the rms distortion does not increasesignificantly at the resonant frequency of the input filter. Bycomparison, FIG. 25 shows the same current components under identicaloperating conditions for the case of frequency angle δ equal to 30degrees (δ/2=15°). As earlier stated, this value of δ results in equalshorting intervals, i.e., equally spaced conduction intervals. The largeresonant amplification of the component with frequency 5f_(I) +6f_(O)and the correspondingly large input supply current distortion, arevisible from curve (1) in FIG. 25.

It is proposed to apply the technique minimizing of the input currentdistortion by controlling the position of the conduction intervalswithin the basic time frame T with an increased number of conductionintervals. FIG. 26 shows the "triple-pulse" situation (three conductionintervals of duration β within a time frame T of 60°) and FIG. 27 the"quadruple-pulse" situation (four conduction intervals of duration βwithin a time frame T of 60°) (δ defines the distance of the outer pulseaxis from the center pulse axis in the three-pulse case; δ₁ and δ₂define the distances of the inner and outer pulses from the centralaxis, in the four-pulse case).

Specific values of angle δ which result in zero amplitude for one of thedominant output voltage and input current harmonics are shown in TableII herebelow for the "triple-pulse" pattern, and specific values ofangles δ₁ and δ₂ (those angles defining the distance to the mirror-imageaxis of the inner and outer pulse axes, respectively) are shown in TableIII for the "quadruple-pulse" pattern.

                  TABLE II                                                        ______________________________________                                        Value of Angle δ/2                                                                       Component Eliminated                                         ______________________________________                                        24.00°    6f.sub.I + 5f.sub.O (output voltage)                                          5f.sub.I + 6f.sub.O (input current)                          17.14°    6f.sub.I + 7f.sub.O (output voltage)                                          7f.sub.I + 6f.sub.O (input current)                          ______________________________________                                    

                  TABLE III                                                       ______________________________________                                        Value of δ.sub.1                                                                  Value of δ.sub.2                                                                    Component Eliminated                                    ______________________________________                                        9.25°                                                                            26.60°                                                                             6F.sub.I + 5f.sub.O (output voltage)                                          5f.sub.I + 6f.sub.O (input current)                     4.34°                                                                            21.91°                                                                             6f.sub.I + 7f.sub.O (output voltage)                                          7f.sub.I + 6f.sub.O (input current)                     ______________________________________                                    

The variations of angle δ required for minimum input current distortionwith the "triple-pulse" pattern of FIG. 26 are illustrated in FIG. 28for the previously defined input filter (f_(r) /f_(I) =6, Q=10). Thecorresponding input current components and minimized supply currentdistortion are shown in FIG. 29.

The variations of angles δ₁ and δ₂ required for minimum input currentdistortion with the "quadruple-pulse" pattern of FIG. 27 are shown inFIG. 30. The relevant input current components and minimized supplycurrent distortion are shown in FIG. 31.

It is clear that the angles (δ₁ and δ₂) determining the location of theconduction intervals in the basic time frame can be controlled so as tooptimize the input supply current distortion and meet differentrequirements while accommodating different input filter characteristics.

As disclosed in the prior art, and illustrated in FIG. 7, when effectingAC motor speed control, the relative length of time interval t₁decreases and that of t₂ increases, within the time frame T, which alsoincreases as the output frequency of the UFC is decreased, in order tokeep the output frequency to voltage ratio, thereby to maintain theairgap flux in the motor approximately constant. As earlier explainedwith the prior art UFC, increasing the time duration T, and decreasingthe time interval ratio t₁ /t₂ result in significantly increased rippleboth in the motor and input supply currents at relatively low outputfrequencies. On the other hand, at relatively high output frequencies,for which the fundamental output voltage is close to its maximum value,time interval t₁ becomes longer than t₂, so that voltage control nolonger has any significant effect on the ripple of the output and inputcurrents.

Applying the voltage control method in the context of the invention,since the basic time frame T is subdivided into n subtime frames T^(*)(each with a t₁ ^(*) and a t₂ ^(*) interval during which load is eitherconnected to the AC input supply or it is shorted) the switching rate ofthe power devices in the UFC is increased n times. In a practical UFCmotor drive system, the output frequency may be controlled typically inthe range of zero to 2 times the input frequency. This would require tovary the basic time frame T e.g. T=1/6(f_(I) +f_(O)) from T=1/(6f_(I))(zero output frequency) to T=1/(18f_(I)). In other words, the length ofT at the maximum output frequency (f_(O) max =2f_(I)) is one-third ofthat at the minimum output frequency (f_(O) min =0). This means that theswitching rate of the power devices increases by a factor of three atthe maximum output frequency.

Taking into account the fact that earlier and more conventional UFCvoltage control has an adverse effect on the output and input currentripples primarily at relatively low output frequencies, and that theswitching rate of the power devices in a UFC cannot be made arbitrarilyhigh for practical reasons (for example, switching losses), it isconcluded that a voltage control method in which the number, n, ofsubtime frames, T^(*), is varied with the length of time frame T,provides the best practical solution. With this arrangement, both theoutput/input current ripple and the switching rate of the power devicesin the UFC can be kept within reasonable limits over the total outputfrequency range.

To summarize with the latter method of UFC output voltage control, thebasic time frames T, during which the input supply voltages are insequence connected to the output, are subdivided into n (where n is aninteger number greater than one) subtime frames T^(*). ##EQU34## Eachsubtime frame T^(*) is further divided into two time intervals t₁ ^(*)and t₂ ^(*). During time intervals t₁ ^(*), within a given time frame T,the load is connected to the same phase of the input voltage by the UFCpower switches. During time intervals t₂ ^(*), the output isdisconnected from the input supply and the load is shorted by the UFCpower switches. The amplitude of the fundamental output voltage isapproximately proportional to the ratio: ##EQU35## The number of subtimeframes determined by integer n, that is, the number of conductionintervals within the time frame T, is varied as a function of T (n isdecreased with increasing T) in such a way that the ratio of: ##EQU36##which determines the amplitude of the fundamental output voltage,remains the same at a given T independently of n. This advantage isadded to the advantage due to the invention where the locations of theconduction intervals are changed within the basic time frame, as theoutput frequency is varied, in such a way that the distortion of thecurrent drawn by the UFC from the AC supply is minimized.

This technique, namely by control of the locations of the conductionintervals within the basic time frame, can be used also to eliminatesome of the harmonic components from the output voltage wave, or ingeneral, to minimize the output distortion according to some givencriterion.

FIG. 32 is a block diagram showing a digital control circuit accordingto the invention which generates GTO drive signals from distributor 28on lines 32 to the 18 GRO's of the UFC converter so as to implement thepreviously described UFC control strategy.

FIG. 33 shows under (f) how the four pulses in a quadruple-pulsesituation are generated, each within a fourth of the basic time period Tin order to provide with counts (α₁, α₂) for the first pulse, (α₃, α₄)for the second, (α₅, α₆) for the third and (α₇, α₈) for the fourth pulsea distributed occurrence, like in FIG. 27 of proper width (α₂, α₄, α₆,α₈ respectively) and proper occurrence (α₁, α₃, α₅ and α₇). Similarlyunder (g) in a three-pulse situation, from T/4 are defined theoccurrences of the front and tail edge (α₁, α₃) of one pulse, of thesecond pulse (α₃ +α₄ and α₅), of the third pulse (α₅ +α₆ and α₇), thusdefining the location and the width.

Finally under (h) from T/4 are defined the occurrence of the front edge(α₁ and α₅ for the respective pulses) and the occurrence of the tailedge (α₃ and α₇ for the respective pulses) in a two-pulse situation,thereby defining location and width of the two pulses.

Referring again to FIG. 32, the desired output frequency, f_(O) of line10 and the input frequency, f_(IN) of line 11 are summed as analogquantities and the sum of line 12 is converted into a pulse train online 14 of frequency 6120* (f_(O))+f_(IN)) by a voltage-controlledoscillator (VCO). This step could also be done digitally if desired byprogramming counters with digital numbers. The output frequency, f_(O)of line 10, is also used to specify on line 17 the desired outputvoltage V_(O), so that V_(O) /f_(O) is maintained constant as generallydone in an AC motor drive, although, as will be described later, suchV_(O) /f_(O) ratio may be altered to provide a voltage "boost" at lowfrequencies. The VCO output pulse train of line 14 serves as the controlcircuit clock to provide synchronous operation of all subsequentoperations. Thus, from line 14 by line 46 to presettable counter 52, byline 48 to lock-out counter 55, line 49 to flip-flop 54, and by line 45to latching device 31 buffering distributor 28 of the drive signals ofline 32. The clock signal is by line 15 and programmable counter 21divided in sequence by 255, then by divider 23 it is divided by 4 and bydivider 50 it is divided by 6. The input pulse train of line 15ultimately produces on lines 25 the required (f_(OUT) +f_(IN)) controlsignals from pins Q_(A2), Q_(B2), and Q_(C2) of device 50. The inputpulse train of line 24 to the divide-by-six counter 50 is the period Tof the basic UFC switching interval. The input pulse train of line 22 tothe divide-by-four counter 23 has the period T/4, namely the intervalassociated with the quadruple-pulse modulation mode. The input pulsetrain of line 15 to the divide by 255 counter 21 has a period whichcorresponds to T/1020, or 360/6120 electrical degrees of the (f_(OUT)+f.sub. IN) switching frequency. Therefore, each clock pulse from theVCO represents 0.059 electrical degrees of the switching frequency and,for this embodiment of the control circuit, it represents the resolutionto which any pulse width, or pulse position, can be specified.

The desired output voltage V_(O), of line 17 is converted by an A/Dconverter 10 into an eight-bit digital value at pins D₀ -D₇ which isconcatenated with the subinterval T/4 from line 22 and line 61 toaddress pin A_(O) of ROM 51 to address a look-up table stored in the 2Kby 8 wide ROM device. Pins D₀ -D₇ define by lines 56 the address pins A₁-A₈ for the ROM. This ROM sequentially outputs on output pins D₀ -D₇ andline 62 values which are appropriate to each of the T/4 intervals, asinputs D₀ -D₇ to a presettable eight-bit counter 52. Counter 52 can alsoreload itself via lines 22, 61, 61' on OR device and line 53 once withineach T/4 interval.

Referring now to FIG. 33, the clock pulses of line 14, the basicsubintervals T/4 of lines 57 as defined by Q_(A1) and Q_(B1) and thestatus of Q_(A1), Q_(B1) are shown under (a), (b), (c) and (d),respectively. Also shown are the basic UFC switching frequency, T, under(e) and three examples of the signal M of line 66 for the quadrupleunder (f), triple under (g) and double pulse under (h) cases,respectively. Not shown is the single pulse case which can easily beconceived from the preceding cases.

Referring concurrently to FIGS. 32 and 33 and illustratively to thequadruple-pulse case, at the first T/4 interval defined by Q_(A1)=Q_(B1) =φ, a preset value corresponding to the time interval α₁representing pulse location within the time frame T is loaded intocounter 52. Counter 52 is loaded synchronously when the T/4 pulse ishigh with a value which is given by (255-α₁) It is the equivalent pulsecount of desired angular position divided by 0.059 and rounded to thenearest integer value. After counter 52 has received α₁ clock pulses acarry out is generated by line 65 which causes the J-K flip flop 54 totoggle. Since flip flop 54 was cleared to zero by line 80' at thebeginning of the interval T, the M signal of line 66 becomes positivefor the duration α₁. Counter 52 also reloads itself with the next value,(255-α₂), which defines the pulse-width. This value is pointed to vialines 62 by the ROM addressed at the next contiguous locations, due toT/4 on line 61 now being a logical low. The M signal, then, is positivefor the pulse duration of α₂ counts, until it toggles low. Thepresettable counter 52 now will remain quiescent for the remainder ofthe T/4 subinterval, due to a disabling signal via lines 70, 71 (thelatter over an inverter) generated by a lock-out counter 54. At the nextsubinterval T/4, by line 61" the lock-out counter 55 is set to a valueof D₁₆ to allow the presettable counter 52 to operate and set and/orreset the M signal of line 66 as desired, e.g. for the α₃ location valueand the α₄ pulse-width value, for the subsequent pulse.

At subsequent T/4 subintervals, the M signal is toggled by flip flop 54and counter 52 is loaded with corresponding α's as necessary to generatethe required M signal in a manner identical to that just described. Atthe end of the T interval, by lines 24, 80, 80', the J-K flip flop 54 iscleared so that a new T interval may be begun, and by line 80" the A/Dconverter 18 is allowed to present its new value of V_(O) at this timeas well.

The presettable counter 52 may be loaded with φφ, in which case 256pulses will be required to toggle the M signal. Since only 255 pulsesare available in each T/4 subinterval, it is possible to delete one, orboth, edge transitions of the M signal, if desired within anysubinterval. This is required for operation in the triple, double, andsingle pulse modes. For a triple-pulse situation, for the example shown,the α₂ and α₈ transitions are deleted by loading the counter with φφ inthe appropriate ROM locations of device 51. For the double-pulsesituation α₂, α₄, α₆, and α₈ transitions are deleted.

The M signal of line 66 is associated in ROM device 28 as pin A_(O) withthe (f_(O) +f_(IN)) signals (Q_(A2), Q_(B2) and Q_(C2)) of pins A₁ -A₃(from lines 25) to point to another look-up function of the ROM andgenerate on lines 30 the command signals which determine the drivesignals of lines 32 to the GTO's. The output of ROM 28 is buffered by alatch 31 to eliminate "glitches" caused by the finite access time of theROM. As shown in FIGS. 6A-6C only six unique drive signals need begenerated, since the same signals are used in each phase of the UFC,although with different switch assignments. The 64 by 6 ROM device 28also has address lines dedicated to the full "on" and off states asprescribed by line 26 in order to provide maximum output voltage andfault protection respectively.

FIG. 34 is a block diagram of the UFC control circuit according to theinvention in the preferred embodiment thereof.

More specifically, the VCO is a 4046 solid state device. Counters 16,21, 23 and 50 are LS163A devices. A/D converter 10 is a solid statedevice known as ADC0800. Device 51 is a 2K×8 ROM of the type 2716. The8-stage presettable counter 52 is comprised of two identical devices74LS163A. Lock-out counter 55 is also a 74LS163A device. ROM 28 is a1K×8 ROM of the type 2708. Latch device 31 is a 74LS374 device.

The full ON and the OFF conditions of lines 26, 27, respectively, intopins A₅ and A₄ of device 28 are derived from the negative Q outputs ofsolid state devices 71, 72, respectively which are of the type 74LS74.These are clocked via line 40 and line 14. The maximum volts is appliedon the CLR pin of device 71, whereas a gate pulse suppress signal isapplied on the CLR pin of device 72.

In Appendix A are grouped the software elements for the calculation ofthe solutions to the function matrix, the determination of the minimumpoints and the determination of the objective functions in the double-,triple- and quadruple-pulse situations. ##SPC1## ##SPC2##

We claim:
 1. In a frequency conversion apparatus having a plurality ofphase-related static converters each coupled between a polyphase ACpower source of frequency f_(IN) and a polyphase AC output power supplyof frequency f_(O), including:for each of said converters a plurality ofcontrollable bilateral switching units controlled for conduction insuccession during a time period (TP) characterizing said frequencyf_(O), each switching unit having a controllable conduction timeinterval (t) within a common time frame T defined by a controllablerepetition rate, and occurring through said succession at saidrepetition rate to derive energy from said AC power source through theassociated converter during successive segments of voltage, on a phasebasis, and to apply the derived voltage segments of said succession tosaid output so as to form with associated like pluralities of converterswitching units an AC polyphase power supply therefore; the frequencyf_(O) of said AC power supply being a function of the difference betweenthe frequency f_(IN) of said AC power source and said repetition rate;the combination of: means synchronized with said repetition rate andoperative on said controllable conduction time interval (t) forestablishing with said succession of switching units n elementaryconduction time intervals (t*) distributed throughout the time frame (T)of operation of each switching unit in said succession and occurring ata rate which is n times said repetition rate, n being an integer, thesum of said elementary conduction time intervals (t*) within such timeframe (T) being equal to said controllable conduction time interval (t);means for establishing selected phase positions for said n individualtime intervals (t*) within said time frame (T) to distribute said n timeintervals (t*) unequally through said time frame T so as to minimize atleast one frequency component of the harmonics reflected back to said ACpower source; and means for controlling the switching units of saidsuccession independently and concurrently as a single-pulse-widthmodulated apparatus in relation to a desired frequency f_(O) and adesired output voltage V_(O).
 2. The apparatus of claim 1 with saidphase positions being selected to cancel out one selected frequencycomponent.
 3. The apparatus of claim 1 with a lowpass input filter beinginserted between said AC power source and the input of the saidapparatus, said phase positions being selected to minimize the frequencycomponents below the cut-off response of said lowpass filter.
 4. Theapparatus of claim 3 with said filter being a low pass LC input filter.5. The apparatus of claim 1 with said AC power source and said AC outputbeing three-phase systems; the frequencies of the harmonic componentsbeing given by:

    f.sub.n input current=6.sub.m f.sub.O +(6m±1)f.sub.I

where m=1, 2, . . . etc.; with n=2, said two time intervals (t*) being amirror image of one another within said time interval (T), a distance δfrom one another axis to axis and having a width β, the distance δ beingchosen so as to eliminate specific frequency components in the inputcurrent from said AC power source.
 6. The apparatus of claim 5 with T=60electrical degrees, and δ/2=18°, thereby to eliminate (6f_(I) +5f_(fO))in the output voltage and (5f_(I) +6f_(O)) in the input current.
 7. Theapparatus of claim 5 with T=60 electrical degrees, and δ/2=12.86°,thereby to eliminate (5f_(I) +7f_(O)) in the output voltage, and (7f_(I)+6f_(O)) in the input current.
 8. The apparatus of claim 5 with T=60electrical degrees, and δ/2=8.18°, thereby to eliminate (2f_(I)+11f_(O)) in the output voltage and (11f_(I) +12f_(O)) in the inputcurrent.
 9. The apparatus of claim 5 with T=60 electrical degrees, andδ/2=6.92°, thereby to eliminate (12f_(I) +13f_(O)) in the outputvoltage, and (13f_(I) +12f_(O)) in the input current.
 10. The apparatusof claim 1 with said AC power source and said AC output beingthree-phase systems; the frequencies of the harmonic components beinggiven by

    f.sub.n input current=6.sub.m f.sub.O +(6.sub.m ±1)f.sub.I

where m=1, 2, . . . etc.; with n=3, said three time intervals (f*)forming a mirror image of one another about the axis of a central one ofthem, within said time interval (T), a distance 2δ between the axis ofthe outer ones of them, said time interval being β wide; the distance δbeing chosen so as to eliminate selected frequency components in theinput current from said AC power source.
 11. The apparatus of claim 10with T=60°, δ/2=240, thereby to eliminate (6f_(I) +5f_(O)) in the outputvoltage and (5f_(I) +6f_(O)) in the input current.
 12. The apparatus ofclaim 10 with T=60°, δ/2=17.14°, thereby to eliminate (6f_(I) +7f_(O))in the output voltage and (7f_(I) +6f_(O)) in the input current.
 13. Theapparatus of claim 1 with said AC power source and said AC output beingthree-phase systems; the frequencies of the harmonic components beinggiven by

    f.sub.n input current=6.sub.m f.sub.O +(6.sub.m ±1)f.sub.IN

where m=1, 2, . . . etc.; with n=4, said four time intervals forming amirror image about the middle ones of said time interval T with twoinner time intervals (t*) at 2δ₁ from one another axis to axis, and twoouter time intervals (t*) at 2δ₂ from one another axis-to-axis, saidtime interval (t*) being β wide; the distance δ₁ and δ₂ being chosen soas to eliminate selected frequency components in the input current fromsaid AC power source.
 14. The apparatus of claim 13 with δ₁ =9.25° andδ₂ =26.60° thereby to eliminate (6f_(I) +5f_(O)) in the output voltageand (5f_(I) +6f_(O)) in the input current.
 15. The apparatus of claim 13with δ₁ =4.34° and δ₂ =21.91° thereby to eliminate (6f_(I) +7f_(O)) inthe output voltage and (7f_(I) +6f_(O)) in the input current.
 16. In afrequency conversion apparatus having a plurality of phase-relatedstatic converters each coupled between a polyphase AC power source offrequency f_(IN) and a polyphase AC output power supply of frequencyf_(O), including:for each of said converters a plurality of controllablebilateral switching units controlled for conduction in succession duringa time period (TP) characterizing said frequency f_(O), each switchingunit having a controllable conduction time interval (t) within a commontime frame T defined by a controllable repetition rate, and occurringthrough said succession at said repetition rate to derive energy fromsaid AC power source through the associated converter during successivesegments of voltage, on a phase basis, and to apply the derived voltagesegments of said succession to said output so as to form with associatedlike pluralities of converter switching units an AC polyphase powersupply therefore; the frequency f_(O) of said AC power supply being afunction of the difference between the frequency f_(IN) of said AC powersource and said repetition rate; the combination of: means synchronizedwith said repetition rate and operative on said controllable conductiontime interval (t) for establishing with said succession of switchingunits n elementary conduction time intervals (t*) distributed throughoutthe time frame (T) of operation of each switching unit in saidsuccession and occurring at a rate which is n times said repetitionrate, the sum of said elementary conduction time intervals (t*) withinsuch time frame (T) being equal to said controllable conduction timeinterval (t) n being an integer in relation to the output frequency ofsaid AC power supply; means for initiating each time interval (t*) insuccession at respective selected delays beyond the initiation ofcorresponding fractional time intervals T/n, said delays being chosenwithin such fractional time interval T/n so as to eliminate a selectedfrequency component in the input current from said AC power source;means for terminating each of said time intervals (t*) to establish acontrolled duration thereof, so as to control the output voltage; saidtime intervals (t*) being unequally spaced and of unequal duration whilebeing symmetrically disposed about the middle axis of said time frame(T); and means for controlling said repetition rate to control theoutput frequency.
 17. The apparatus of claim 16 with ROM means forstoring functions representing the front edge occurrence and the tailedge occurrence of said time intervals (t) counted from the initiationof the corresponding fractional time interval T/n and representing theduration of such time intervals (t) as a function of the desired outputvoltage;means for generating a train of pulses in relation to (f_(O)+f_(I)) and for generating with said pulses said fractional timeintervals T/n to control said ROM means, and means for controlling theswitching units of said succession each one n times before controllinganother, in response to said ROM means.